Revisiting nonrelativistic limits of field theory: Antiparticles

TL;DR

This paper explores the nonrelativistic limits of various field theories, including scalar and Dirac fields, emphasizing the simultaneous emergence of particles and antiparticles and analyzing implications for dark matter models.

Contribution

It develops a formalism for the nonrelativistic limit of antiparticles and addresses issues in non-local approaches, extending understanding of field theory limits.

Findings

Nonrelativistic limit of Dirac equation includes particles and antiparticles.

Potential effects on axion dark matter models are analyzed.

Problems in non-local approaches are discussed.

Abstract

Different subtleties and problems associated with a nonrelativistic limit of the field theory to the Schroedinger theory are discussed. In this paper, we revisit different cases of the nonrelativistic limit of a real and complex scalar field in the level of the Lagrangian and the equation of motion. We develop the nonrelativistic limit of the Dirac equation and action in the way that the nonrelativistic limit of spin-$\frac{1}{2}$ wave functions of particles and antiparticles appear simultaneously. We study the effect of a potential like $U(\phi)\propto \phi^4$ which can be attributed to axion dark matter field in this limit. We develop a formalism for studying the nonrelativistic limit of antiparticles in the quantum mechanics. We discussed the non-local approach for the nonrelativistic limit and its problems.